residueclass
A residue class modulo n, for a positive integer n, is the set of all integers that are congruent to a given integer a modulo n. Formally, it is the set {a + nk : k ∈ Z}. It is denoted [a]_n or a mod n. The residue class contains all integers that share the same remainder when divided by n.
The collection of all residue classes modulo n partitions the integers into n disjoint classes: [0]_n, [1]_n,
Canonical representatives are commonly taken to be the least nonnegative residues in {0, 1, ..., n−1}, though
Beyond integers, the concept generalizes to any ring R with an ideal I: the residue classes modulo
Residue classes are fundamental in number theory and its applications. They underpin solving congruences, the Chinese